aa5 A water tower has the geometry shown in the figure the t

A water tower has the geometry shown in the figure (the tower part is a cylinder with radius R and height h, and the upper part is a half sphere with radius R). Determine the radius R if h = 10 m and the volume is 1.050 m^3. (Write an equation for the volume in terms of the radius and the height. Solve the equation for the radius, and use the double command to obtain a numerical value. Consider the following set of seven equations from a loop mesh circuit, with I representing current. Define a symbolic variable for each of the equations, and use MATLAB symbolic capability to solve for each unknown current. Let the following polynomial represent the altitude of the flapping wing aerial vehicle during the first 48 seconds of a surveillance operation. h(t) = -0.12t^4 + 12t^3 - 380t^2 + 4100 + 220 (m) Use MATLAB to determine the equation for velocity of the vehicle Use MATLAB to determine the equation for acceleration of the vehicle Use MATLAB to determine when the vehicle hits the ground. As the position equation is a 4\'h order polynomial, there will be four answers. Find the correct answer from them. Use MATLAB symbolic plotting capability to create plots of altitude, velocity, and acceleration from time 0 until the vehicle hits the ground. Note that you will need three separate plots, since altitude, velocity, and acceleration have different units. Determine the maximum height reached by the vehicle.

Solution

Given,

V= Volume of Water Tank = 1050 m³

h= Height = 10 m

Volume of Water Tank = Volume of Cylinder + Volume of hemi-Sphere

Volume of Water Tank= V = *R² *h + ½*(4**R³)

Now,

Matlab code for solving above equation is

Pi=3.1416;

h=10;

V=1050;

X= double([2*Pi,Pi*h,0,-V]);

R= roots(X)

Output:

R =

-4.6252 + 4.2338i

-4.6252 - 4.2338i

   4.2504 + 0.0000i

Result: As radius can’t be imaginary

Radius of Cylinder is 4.2504 m